Method and system for baseband predistortion linearization in multi-channel wideband communications systems

ABSTRACT

An efficient baseband predistortion linearization method for reducing the spectral regrowth and compensating memory effects in wideband communication systems using effective multiplexing modulation technique such as wideband code division multiple access and orthogonal frequency division multiplexing is disclosed. The present invention is based on the method of piecewise pre-equalized lookup table based predistortion, which is a cascade of a lookup table predistortion and piecewise pre-equalizers.

CROSS-REFERENCES TO RELATED APPLICATIONS

The present application is a continuation of U.S. patent applicationSer. No. 13/404,679, filed on Feb. 24, 2012, entitled “METHOD AND SYSTEMFOR BASEBAND PREDISTORTION LINEARIZATION IN MULTI-CHANNEL WIDEBANDCOMMUNICATION SYSTEMS,” now U.S. Pat. No. 8,509,347, which is acontinuation of U.S. patent application Ser. No. 11/961,969 filed onDec. 20, 2007, entitled “METHOD AND SYSTEM FOR BASEBAND PREDISTORTIONLINEARIZATION IN MULTI-CHANNEL WIDEBAND COMMUNICATION SYSTEMS,” now U.S.Pat. No. 8,149,950, which claims the benefit under 35 USC 119(e) of U.S.Provisional Patent Application No. 60/877,035, filed Dec. 26, 2006, andU.S. Provisional Patent Application No. 61/012,416, filed Dec. 7, 2007,the contents of which are hereby incorporated by reference in theirentirety.

BACKGROUND OF THE INVENTION

The linearity and efficiency of radio frequency (RF) power amplifiers(PAs) have been a critical design issue for non-constant envelopedigital modulation schemes which have high peak-to-average-power ratios(PARs) as the importance of spectral efficiency in wirelesscommunication systems increases. RF Pas have nonlinearities thatgenerate amplitude modulation-amplitude modulation (AM-AM) and amplitudemodulation-phase modulation (AM-PM) distortion at the output of the PA.These effects create spectral regrowth in the adjacent channels andin-band distortion which degrades the error vector magnitude (EVM).

The relationship between linearity and efficiency is a tradeoff sincepower efficiency is very low when the amplifier operates in its linearregion and increases as the amplifier is driven into its compressionregion. In order to enhance linearity and efficiency at the same time,linearization techniques are typically applied to the RF PAs. Variouslinearization techniques have been proposed such as feedback,feedforward and predistortion.

One technique is baseband digital predistortion (PD) which typicallyuses a digital signal processor. Digital predistortion can achieveimproved linearity and improved power efficiency with reduced systemcomplexity when compared to the widely used conventional feedforwardlinearization technique. A software implementation provides the digitalpredistorter with re-configurability suitable for multi-standardsenvironments. In addition, a PA using an efficiency enhancementtechnique such as a Doherty power amplifier (DPA) is able to achievehigher efficiencies than traditional PA designs at the expense oflinearity. Therefore, combining digital predistortion with a PA using anefficiency enhancement technique has the potential to improve systemlinearity and overall efficiency.

However, most digital PDs presuppose that PAs have no memory or a weakmemory. This is impractical in wideband applications where memoryeffects cause the output signal to be a function of current as well aspast input signals. The sources of memory effects in PAs includeself-heating of the active device (also referred to as long timeconstant or thermal memory effects) and frequency dependencies of theactive device, related to the matching network or bias circuits (alsoreferred to as short time constant or electrical memory effects). Assignal bandwidth increases, memory effects of PAs become significant andlimit the performance of memoryless digital PDs.

Various approaches have been suggested for overcoming memory effects indigital PDs. For the short-term memory effects, a Volterra filterstructure was applied to compensate memory effects using an indirectlearning algorithm, but the number of optimization coefficients is verylarge as the order increases. This complexity makes the Volterra filterbased PD extremely difficult to implement in real hardware. A memorypolynomial structure, which is a simplified version of the Volterrafilter, has been proposed in order to reduce the number of coefficients,but even this simplified version still requires a large computationalload. In addition, such a memory polynomial based PD suffers from anumerical instability when higher order polynomial terms are includedbecause a matrix inversion is required for estimating the polynomialcoefficients. An alternative, yet equally complex structure based onorthogonal polynomials has been utilized to alleviate the numericalinstability associated with the traditional polynomials. To furtherreduce the complexity at the expense of the performance, the Hammersteinpredistorter, which is a finite impulse response (FIR) filter or alinear time invariant (LTI) system followed by a memoryless polynomialPD, has been proposed. The Hammerstein predistorter assumed that the PAmodels used follow a Wiener model structure which is a memorylessnonlinearity followed by a finite impulse response (FIR) filter or alinear time invariant (LTI) system.

This implementation means that the Hammerstein structure can onlycompensate for memory effects coming from the RF frequency response.Therefore, if the RF frequency response is quite flat, the HammersteinPD cannot correct for any other types of memory effects, such asbias-induced and thermal memory effects.

Most recently, a static lookup table (LUT) digital baseband PD cascadedwith a sub-band filtering block has been used in order not to compensatefor electrical memory effects, but to combat gain and phase variationdue to temperature changes of the PA after an initial setting for thefixed LUT PD.

Hence, there has been a long-felt need for a baseband predistortionlinearization method able to compensate for not only RF frequencyresponse memory effects but also bias-induced or thermal memory effectsin multi-channel wideband wireless transmitters.

SUMMARY OF THE INVENTION

Accordingly, the present invention substantially overcomes many of theforegoing limitations of the prior art, and provides a system and methodof baseband predistortion linearization that compensates fornonlinearities as well as memory effects found in multi-channel widebandwireless transmitters. This result is achieved through the use ofpiecewise pre-equalized PD utilizing a lookup table. With this approach,the present invention is able to compensate for electrical and thermalmemory effects while at the same time reducing the computationalcomplexity and the numerical instability of the system as compared withprior art systems using a memory polynomial PD algorithm, while thepresent invention is comparable to a memory polynomial PD in terms ofthe resulting linearity in the performance of a multi-band PA.

Further objects and advantages of the invention can be more fullyunderstood from the following detailed description taken in conjunctionwith the accompanying drawings in which:

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram showing a piecewise pre-equalized LUTpredistortion system in accordance with the invention.

FIG. 2 is a schematic diagram showing a polynomial-based embodiment ofthe equalizer 107 of FIG. 1.

FIG. 3A is a graph showing complex gain adjuster response.

FIG. 3B is a graph showing piecewise equalizer response in accordancewith the invention.

FIG. 3C is a graph showing response of the cascade of complex gainadjuster and piecewise equalizers in accordance with the invention.

FIG. 3D is a graph showing a power amplifier response

FIG. 3E is a graph showing detailed response from the response of thecascade of complex gain adjuster and piecewise equalizers and thecomplex gain adjuster response.

FIG. 4A is a graph showing representative linearization results beforeand after linearization with an embodiment of a memoryless LUT PD usingan eight tone test signal with 500 kHz spacing.

FIG. 4B is a graph showing representative linearization results beforeand after linearization with a LUT Hammerstein PD using an eight tonetest signal with 500 kHz spacing.

FIG. 4C is a graph showing representative linearization results beforeand after linearization with a piecewise pre-equalized PD of the presentinvention using an eight tone test signal with 500 kHz spacing.

FIG. 4D is a graph showing representative linearization results beforeand after linearization with a memory polynomial PD using an eight tonetest signal with 500 kHz spacing.

FIG. 5 is a graph showing representative linearization results for thefour types of PDs consisting of a memoryless LUT PD, a LUT HammersteinPD, a piecewise pre-equalized PD of the present invention, and a memorypolynomial PD using a single W-CDMA carrier, respectively.

FIG. 6 is a graph showing performance comparisons of the simulationresults of the ACPR for the four types of PD consisting of a memorylessLUT PD, a LUT Hammerstein PD, a piecewise pre-equalized PD of thepresent invention, and a memory polynomial PD using a single W-CDMAcarrier, respectively.

FIG. 7 is a graph showing measured linearization results for the 4 typesof PD consisting of a memoryless LUT PD, a LUT Hammerstein PD, apiecewise pre-equalized PD of the present invention, and a memorypolynomial PD using a single W-CDMA carrier, respectively.

FIG. 8 is a graph showing performance comparisons of the measurementresults of the ACPR for the 4 types of PD consisting of a memoryless LUTPD, a LUT Hammerstein PD, a piecewise pre-equalized PD of the presentinvention, and a memory polynomial PD using a single W-CDMA carrier,respectively.

FIG. 9 is a graph showing complexity estimation of the piecewisepre-equalized PD of the present invention.

FIG. 10 is a graph showing complexity estimation of the memorypolynomial PD.

DETAILED DESCRIPTION OF THE INVENTION

To overcome the computational complexity and numerical instability ofthe memory polynomial PD found in the prior art, The present invention,therefore, utilizes an adaptive LUT-based digital predistortion systemwith a LUT that has been pre-equalized to compensate for memory effects,so as to achieve less computational load than the prior art while alsoreducing the adjacent channel power ratio (ACPR) to substantially thesame degree as the memory polynomial PD has achieved. The systemprovided by the present invention is therefore referred as a piecewisepre-equalized, lookup table based predistortion (PELPD) systemhereafter.

Preferred and alternative embodiments of the PELPD system according tothe present invention will now be described in detail with reference tothe accompanying drawings.

FIG. 1 is a schematic diagram showing an embodiment of a PELPD system inaccordance with the invention. As illustrated, the linear magnitudeaddressing method for the LUT 106 indexing is used as follows:m=round(|u(n)|·N),where u (n) is the input signal 101 and the round function returns thenearest integer number which is the index (m) and N is the LUT 106 size.

The digital complex baseband input signal samples 101 are multipliedprior to pre-equalization 107 by complex coefficients 102 drawn from LUTentries as followsx(n)=u(n)·F _(m)(|u(n)|),where F_(m)(|u(n)|) is the complex coefficient 102 corresponding to aninput signal 101 magnitude for compensating AM to AM and AM to PMdistortions of the PA 110.

N by K−1 filter coefficients in the LUT of the piecewise pre-equalizer107 are used to compensate for memory effects, where N is the depth ofthe LUT and the FIR filter has K taps. In some embodiments, thepiecewise pre-equalizers 107 use a FIR filter rather than an infiniteimpulse response (IIR) filter because of stability issues, although aFIR filter is not necessarily required for all embodiments. The output104 of the pre-equalizers can be described by

$\begin{matrix}{{z(n)} = {\sum\limits_{k = 0}^{K - 1}{{W_{k}^{m}\left( {{u(n)}} \right)} \cdot {x\left( {n - k} \right)}}}} \\{{= {\sum\limits_{k = 0}^{K - 1}{{W_{k}^{m}\left( {{u(n)}} \right)} \cdot {u\left( {n - k} \right)} \cdot {F_{m}\left( {{u\left( {n - k} \right)}} \right)}}}},}\end{matrix}$

where W_(k) ^(m)(|(n)|) is the k-th tap and m-th indexed coefficientcorresponding to the magnitude of the input signal, u(n) 101. Also,W_(k) ^(m)(|u(n)|) is a function of |u(n)| and F_(m) 102 is a functionof (|u(n−k)|. For analysis purposes, the memoryless LUT 106 (F_(m))structure can be replaced by a polynomial model as follows:

${F_{m}\left( {{u(n)}} \right)} = {\sum\limits_{p - 1}^{P}{b_{{2p} - l} \cdot {{u\left( {n - k} \right)}}^{2{({p - 1})}}}}$

where 2p−1 is the polynomial order and b is a complex coefficientcorresponding to the polynomial order. Moreover, it is noted that thetap coefficients and memoryless LUT coefficients (Fm) 102 depend on u(n)and u(n−k), respectively.

Therefore, each piece of the equalizer can be expressed using apolynomial equation by

${z(n)} = {\sum\limits_{k = 0}^{K - 1}{{W_{k}^{m}\left( {{u(n)}} \right)} \cdot {\sum\limits_{p = 1}^{P}{b_{{2p} - 1} \cdot {u\left( {n - k} \right)} \cdot {{u\left( {n - k} \right)}}^{2{({p - 1})}}}}}}$

where W_(k) ^(m)(|u(n)|) is the k-th tap coefficient with the m-th indexbeing a function of |u(n)|. Without loss of generality, the piecewisepre-equalizers 107 can be defined similarly using a 1-th orderpolynomial,

${z(n)} = {\sum\limits_{k = 0}^{K - 1}{\sum\limits_{p = 0}^{L}{{w_{k,{{2l} - 1}} \cdot {{u(n)}}^{2{({l - 1})}}} \times {\sum\limits_{p - 1}^{P}{b_{{2p} - 1} \cdot {u\left( {n - k} \right)} \cdot {{u\left( {n - k} \right)}}^{2{({p - 1})}}}}}}}$where w_(k,l) is the k-th tap and l-th order coefficient.

After digital-to-analog converting 108 of z(n) 104, this signal isup-converted 109 to RF, amplified by the PA 110 generating distortions,attenuated 113, down-converted 114 to baseband, and then finallyanalog-to-digital converted 115 and applied to the delay 116 estimationalgorithm 117. The feedback signal, that is, the output of the PA 110with delay, y(n−Δ) 105 can be described byy(n−Δ)=G(|z(n−Δ)|)·e ^(j·Φ(|z(n−Δ)|))

where G(•) and Φ(•) is AM/AM and AM/PM distortions of the PA 110,respectively and Δ is the feedback loop delay. For estimating Δ, acorrelation technique was applied as follows:

${R(d)} = {\frac{1}{N}{\sum\limits_{n = 0}^{N - 1}{{z(n)} \cdot {y^{*}\left( {n + d} \right)}}}}$where d is the delay variable and N is the block size to correlate.

After delay 116 estimation, the memoryless LUT 106 coefficients can beestimated by the following equation which is the least mean square (LMS)algorithm with indirect learning.F _(m)(|u(n+1)|=F _(m)(|u(n)|)+μ·u(n)·e(n)where n is the iteration number, μ is the stability factor and e(n) isx(n)−y(n)·F_(m)(|x(n)|).

It should be pointed out that addressing already generated can be reusedfor indexing y(n) 105 which is a distorted signal able to cause anothererror due to incorrect indexing. During this procedure, the samples,x(n) 103, should bypass by the piecewise pre-equalizers 107. Afterconvergence of this indirect learning LMS algorithm, the equalizers 107are activated. An indirect learning method with an LMS algorithm hasalso been utilized for adaptation of the piecewise filter coefficients.The input of the multiple equalizers 107 in the feedback path is writtenin vector format asy _(FI)(n)=[y _(F)(n)y _(F)(n−1) . . . y _(F)(n−K+1)]

where y_(F)(n) is the post LUT output, that is, y(n)·F_(m)(|y(n)|).

Therefore, the multiple FIR filter outputs, yFO(n), can be derived invector format using the following equations.y _(FO)(n)=W ^(m) ·y _(FI)(n)^(T)W ^(m) =[W ₀ ^(m) W ₁ ^(m) . . . W _(k-1) ^(m)]

where T is a transpose operator.

Adaptation of the tap coefficients of the pre-equalizers 107 can beobtained as follows:W ^(m)(|u(n+1)|)=W ^(m)(u(n)|)+μ·(y _(FI)(n)^(T))*·E(n)

where E(n) is the error signal between z(n) and yFO(n), and μ is thestep size (* represents the complex conjugate). The adaptation algorithmdetermines the values of the coefficients by comparing the feedbacksignal and a delayed version of the input signal.

Referring to the feedback path beginning at output 111, it will beappreciated that several alternatives exist for using such feedback toupdate the LUT values or polynomial coefficients. In some embodiments,the output of the PA is converted to baseband, and the resultingbaseband signal is compared to the input signal. The resulting error isused to correct the LUT values and coefficients. In other embodiments,the output from the PA is spectrally monitored and the out of banddistortion is monitored using a downconverter, bandpass filter and powerdetector. The power detector value is then used to adjust the LUT valuesor polynomial coefficients.

FIG. 2 illustrates the corresponding block diagram of the piecewisepre-equalizers 107 PD when polynomial equations are utilized. Thepolynomial representation requires too many complex multiplicationssimilar to the Volterra series. The complexity is reduced when aPELPD-based approach, as shown in FIG. 1, is utilized, because fewercalculations are required, although more memory may be required. It willbe appreciated from the discussion herein that the pre-equalizingportion is adaptive and designed to correct memory effects, while thelut serves primarily to pre-distort to correct the other nonlinearitiesfound in commercial PA's.

FIGS. 3A-3D are graphical explanations of the PELPD of the presentinvention. A typical memoryless predistorter response is shown in FIG.3A. FIG. 3B demonstrates the hysteresis created by the piecewisepre-equalizers divided into N pieces. Since the hysteresis of the poweramplifier is not necessarily uniformly distributed over the whole inputmagnitude range, the piecewise pre-equalizers are applied to achieve auniform compensation across the entire input range. The output of thePELPD of the present invention is illustrated in FIG. 3C, which can bethought of as resulting from a cascade of FIGS. 3A and 3B. FIG. 3D showsthe response of a typical power amplifier response and FIG. 3B resultsin the PELPD of the present invention as represented in FIG. 3C. FIG. 3Dshows the response of a typical power amplifier response with memory.The desired linear response in FIG. 3E is achieved after FIG. 3C andFIG. 3D are cascaded.

In order to examine the performance of the PELPD of the presentinvention, the behavioral modeling of a PA based on time domainmeasurement samples was first carried out. The behavioral model wasbased on the truncated Volterra model. A 300 W peak envelope power (PEP)Doherty PA using two 170 W push-pull type laterally diffused metal oxidesemiconductors (LDMOS) at the final stage was designed. This Doherty PAoperates at 2140 MHz band and has 61 dB of gain and 28% power addedefficiency (PAE) at an average 30 W output power. To construct the PAmodel based on measurements of the actual PA, the test bench wasutilized [K. Mekechuk, W. Kim, S. Stapleton, and J. Kim, “LinearinzingPower Amplifiers Using Digital Predistortion, EDA Tools and TestHardware,” High Frequency Electronics, pp. 18-27, April 2004]. Based onthe behavioral model, various types of PDs including a memoryless LUTPD, a Hammerstein PD, the PELPD of the present invention and a memorypolynomial PD have been simulated and the adjacent channel power ratio(ACPR) performances are compared. The LUT size was fixed to 128 entriesthrough all simulations, which is a compromise size consideringquantization effects and memory size. Those skilled in the art willrecognize that the amount of compensation for nonlinearities is relatedto the size of the LUT 106. Increases in LUT size, while yielding a moreaccurate representation of the nonlinearities, comes at the cost of moreeffort in the adaptation. Thus, selection of LUT size is a trade-offbetween accuracy and complexity.

As a test signal, a single downlink W-CDMA carrier with 64 dedicatedphysical channels (DPCH) of Test Mode based on 3rd GenerationPartnership Project (3GPP) standard specifications, which has 3.84Mchips/s and 9.8 dB of a crest factor. First, an eight tone signal with500 kHz spacing which has 9.03 dB of PAR and 4 MHz bandwidth, which iscomparable to a W-CDMA signal, was used for verifying the proposedmethod.

FIGS. 4A-4D are graphs showing representative linearization resultsbefore and after linearization of the four types of PD. As shown in FIG.4A, a conventional memoryless LUT PD was able to improve the linearityand also compensate for the memory effects. FIG. 4B shows a conventionalHammerstein PD which deteriorates the performance above 10 MHz andimproves it within a 10 MHz bandwidth. If the RF frequency response inthe main signal path is quite flat, the Hammerstein PD is not able tocorrect any other memory effects except for frequency response memoryeffects. There is also no obvious improvement for reducing spectralregrowth using the conventional Hammerstein PD. It is very clear thatthe ability of the Hammerstein PD for suppressing distortions comingfrom memory effects is quite limited. FIG. 4C shows the performance ofthe PELPD of the present invention (with 2 taps). FIG. 4D illustratesthe performance of a conventional memory polynomial PD (with 5th orderand two memory terms). By comparing FIGS. 4A-4D, it can be seen that thePELPD of the present invention is comparable to the memory polynomial PDin terms of ACPR performance.

FIG. 5 is a graph showing linearization results for the four types of PDmentioned above. A single W-CDMA carrier was applied to the LUT PD, theLUT Hammerstein PD, the PELPD of the present invention, and the memorypolynomial PD.

FIG. 6 is a graph showing performance comparisons of the simulationresults of the ACPR for the 4 types of, respectively. The conventionalHammerstein PD was unable to improve any distortions coming from memoryeffects over the memoryless PD. The PELPD of the present invention couldsuppress distortions due to nonlinearities as well as memory effects ofthe PA.

After verifying the ACPR performance of the PELPD of the presentinvention in the simulations based on the behavioral PA model, anexperiment was performed using the actual Doherty PA in the test bench.The transmitter prototype consists of an ESG which has two digital toanalog converters (DACs) and a RF up-converter, along with the PA. Thereceiver comprises an RF down-converter, a high speed analog to digitalconverter, and a digital down-converter. This receiver prototype can beconstructed by a VSA. For a host DSP, a PC was used for delaycompensation and the predistortion algorithm. As a test signal, twodownlink W-CDMA carriers with 64 DPCH of Test Model 1 which has 3.84Mchips/s and 9.8 dB of a crest factor was used as the input signal inthe measurements in order to verify the compensation performance of thedifferent PDs. All coefficients of PDs are identified by an indirectlearning algorithm which is considered to be inverse modeling of the PA.During the verification process, a 256-entry LUT, 5 taps FIR filter forHammerstein PD, the PELPD of the present invention (with 2 taps), and a5th order-2 delay memory polynomial were used. The choice of the numberof taps was optimized from several measurements.

FIG. 7 is a graph showing the measured linearization results before andafter linearization of the 4 types of PD using a single W-CDMA carrier,respectively. ACPR calculation at the output of the prototypetransmitter, is performed at a frequency offset (5 MHz and −5 MHz) fromthe center frequency.

FIG. 8 is a graph showing performance comparisons of the measurementresults of the ACPR for the 4 types of PD using a single W-CDMA carrier,respectively. The ACPR value for the transmitter with the Hammerstein PDhaving a 5 tap FIR filter is about 1 dB better than a LUT PD on theupper ACPR (5 MHz offset) and the same at the lower ACPR (−5 MHzoffset). The PELPD of the present invention and a 5th order-2 memorypolynomial PD show close compensation performance in terms of ACPR. Bothare able to improve the ACPR about 4 dB and 6 dB more than HammersteinPD and a memoryless LUT PD, for the lower and upper ACPR, respectively.

The complexity of the PELPD method of the present invention and thememory polynomial method is also evaluated (neglecting LUT readings,writings, indexing, and calculation of the square root (SQRT) of thesignal magnitude, because LUT indexing depends not only on the methods,but also on the variable, for example, magnitude, logarithm, power, andso on and the SQRT operation can be implemented in different ways).Therefore, the complexity is only estimated by counting the number ofadditions (subtractions) and multiplications per input sample. In orderto consider a real hardware implementation, complex operations areconverted into real operations and memory size is also considered. Forexample, one complex multiplication requires two real additions and fourreal multiplications. If N is the number of LUT entries, memory sizerequired is 2N (I&Q LUTs).

FIG. 9 is a graph showing complexity estimation of the PELPD of thepresent invention. If the LUT has 256 entries and the filters have 2taps, the PD requires 40 real additions (subtractions), 54 realmultiplications per sample, and a memory size of 1542. The PELPD of thepresent invention requires the same number of additions andmultiplications as the traditional Hammerstein PD, but requires morememory.

FIG. 10 is a graph showing complexity estimation of the memorypolynomial PD using an RLS indirect learning algorithm. The number ofarithmetic operations are given in FIG. 11, where O is equal to P(K+1).For example, P=5 and K=1 require 1342 real additions (subtractions),1644 real multiplications per sample, and memory size of 24. In acomparison of the number of multiplications with the PELPD of thepresent invention, the memory polynomial PD requires 300 times more realmultiplications per sample. Therefore, the complexity is significantlyreduced by the PELPD method. In addition, the number of realmultiplication for the memory polynomial method grows as the squarepower of the polynomial order and memory length.

In summary, the PELPD of the present invention, compared to theconventional Hammerstein approach, could reduce spectral regrowth moreeffectively and achieve a similar correction capability with the memorypolynomial PD, but requires much less complexity.

Although the present invention has been described with reference to thepreferred and alternative embodiments, it will be understood that theinvention is not limited to the details described thereof. Varioussubstitutions and modifications have been suggested in the foregoingdescription, and others will occur to those of ordinary skill in theart. Therefore, all such substitutions and modifications are intended tobe embraced within the scope of the invention as defined in the appendedclaims.

What is claimed is:
 1. A method of reducing adjacent channel power ratioin a multi-channel wideband communication system, the method comprising:generating an address from a baseband input signal of the communicationsystem; generating a pre-distorted input signal by multiplying thebaseband input signal and an entry retrieved from a memoryless firstlookup table according to the address; and pre-equalizing thepre-distorted input signal using the using one or more pre-equalizationcoefficients retrieved from a second lookup table according to theaddress, the one or more pre-equalization coefficients corresponding tomemory effects in a power amplifier of the communication system.
 2. Themethod of claim 1 wherein each entry in the memoryless first lookuptable comprises a complex coefficient.
 3. The method of claim 2 whereinthe complex coefficient corresponds to amplitude-to-amplitude (AM-to-AM)and amplitude-to-phase (AM-to-PM) distortions of the power amplifier inthe communication system.
 4. The method of claim 1 whereinpre-equalizing the pre-distorted input signal comprises generating aweighted sum of one or more delayed versions of the pre-distorted inputsignal, using the one or more retrieved pre-equalization coefficients asweighting coefficients, each of the one or more delayed versions of thepre-distorted input signal being a product of a respective delayedversion of the baseband input signal and a corresponding entry of thememoryless first lookup table.
 5. The method of claim 1 wherein the oneor more pre-equalization coefficients correspond to filter coefficientsof a finite impulse response filter.
 6. The method of claim 1 whereinthe one or more pre-equalization coefficients correspond to filtercoefficients of an infinite impulse response filter.
 7. The method ofclaim 1 wherein generating an address from the baseband input signalcomprises: computing a product of a magnitude of the baseband inputsignal and a number of entries in the first lookup table; and returninga nearest integer number of the product.
 8. The method of claim 1wherein the one or more pre-equalization coefficients in the secondlookup table are updated using an indirect learning method.
 9. Themethod of claim 8 wherein the indirect learning method uses a least meansquare algorithm.
 10. A system for baseband pre-distortion in amulti-channel wideband communication system, the system comprising: anaddress generator for generating an address from a baseband input signalof the communication system; a memoryless first lookup table for storingone or more entries retrievable according to the address; a secondlookup table for storing one or more pre-equalization coefficientsretrievable according to the address, the one or more pre-equalizationcoefficients corresponding to memory effects in a power amplifier of thecommunication system; and a pre-equalizer for pre-equalizing thebaseband input signal using one or more entries retrieved from thememoryless first lookup table according to the address and one or morepre-equalization coefficients retrieved from the second lookup tableaccording to the address.
 11. The system of claim 10 wherein each entryin the memoryless first lookup table comprises a complex coefficient.12. The system of claim 11 wherein the complex coefficient correspondsto amplitude-to-amplitude (AM-to-AM) and amplitude-to-phase (AM-to-PM)distortions of the power amplifier in the communication system.
 13. Thesystem of claim 10 wherein pre-equalizing the baseband input signalcomprises generating a weighted sum of one or more delayed versions of apre-distorted input signal, using the one or more pre-equalizationcoefficients retrieved from the second lookup table as weightingcoefficients, each of the one or more delayed versions of thepre-distorted input signal being a product of a respective delayedversion of the baseband input signal and a corresponding entry of thememoryless first lookup table.
 14. The system of claim 10 wherein thepre-equalizer comprises a finite impulse response filter.
 15. The systemof claim 10 wherein the pre-equalizer comprises an infinite impulseresponse filter.
 16. The system of claim 10 further comprising afeedback loop for updating the one or more pre-equalization coefficientsin the second lookup table.
 17. The system of claim 16 wherein theupdating is performed using an indirect learning method and a least meansquare algorithm.